Flat BPS Domain Walls on 2d K\"ahler-Ricci Soliton

In this paper we address several aspects of flat Bogomolnyi-Prasad-Sommerfeld (BPS) domain walls together with their Lorentz invariant vacua of 4d N=1 supergravity coupled to a chiral multiplet. The scalar field spans a one-parameter family of 2d K\"ahler manifolds satisfying a K\"ahler-Ricci flow equation. We find that BPS equations and the scalar potential deform with respect to the real parameter related to the K\"ahler-Ricci soliton. In addition, the analysis using gradient and renormalization group flows are carried out to ensure the existence of Lorentz invariant vacua related to Anti de Sitter/Conformal Field Theory (AdS/CFT) correspondence.Comment: 11 pages, 2 tables. Section 3 slightly modifie

Path Independence in Adiabatic Quantum Computing for Hadamard Gate

The computation time in adiabatic quantum computing (AQC) is determined by the time limit of the adiabatic evolution, which in turn depends on the evolution path. In this research we have used the variational method to find an optimized path. For the simplest case involving a single qubit and for the most general path involving one or more independent interpolating functions, the result is path independent. This result does not change when there is an extra Hamiltonian term. We have also applied these two scenarios in AQC to a Hadamard gate. Adding an extra Hamiltonian gives a non-trivial result compared to the normal AQC, however it does not result in a speed-up. Moreover, we show that in these two scenarios we can choose an arbitrary path provided that it satisfies the boundary conditions

Replica Trick Calculation for Entanglement Entropy of Static Black Hole Spacetimes

We calculate the entanglement entropy between two (maximally-extended) spacetime regions of static black hole, seperated by horizon. As a first case, we consider the Schwarzschild black hole, and then we extend the calculations to the charged Reissner- Nordstrom and Schwarzschild-de Sitter black holes with more than one horizon. The case for static and spherically-symmetric solution to the more general F (R) gravity is also considered. The calculation of the entanglement entropy is performed using the replica trick by obtaining the explicit form of the metric which corresponds to the replica spacetime for each black hole under consideration. The calculation of static and spherically-symmetric black holes result in the entanglement entropy that matches the Bekenstein-Hawking area law entropy.Comment: 41 pages, 12 figure

Chaos and fast scrambling delays of dyonic Kerr-Sen-AdS4_4 black hole and its ultra-spinning version

The scrambling time and its delay are calculated using holography in an asymptotically AdS black hole solution of the gauged Einstein-Maxwell-Dilaton-Axion (EMDA) theory, the dyonic Kerr-Sen-AdS$_4$ black hole, perturbed by rotating and charged shock waves along the equator. The leading term of the scrambling time for a black hole with large entropy is logarithmic in the entropy and hence supports the fast scrambling conjecture for this black hole solution, which implies that the system under consideration is chaotic. We also find that the instantaneous minimal Lyapunov index is bounded by $\kappa=2\pi T_H/(1-\mu\mathcal{L})$, which is analogous to the surface gravity but for the rotating shock waves, and becomes closer to equality for the near extremal black hole. For a small value of the AdS scale, we found that the Lyapunov exponent can exceed the bound for a large value of $\mathcal{L}$. Due to the presence of the electric and magnetic charge of the shock waves, we also show that the scrambling process of this holographic system is delayed by a time scale that depends on the charges of the shock waves. The calculations also hold for the ultra-spinning version of this black hole. The result of this paper generalizes the holographic calculations of chaotic systems which are described by an EMDA theory in the bulk.Comment: 19 page

Localized chaos in rotating and charged AdS black holes

The butterfly velocity and the Lyapunov exponent of four-dimensional rotating charged asymptotically AdS black holes are calculated to probe chaos using localized rotating and charged shock waves. The localized shocks also generate butterfly velocities which quickly vanish when we approach extremality, indicating no entanglement spread near extremality. One of the butterfly velocity modes is well bounded by both the speed of light and the Schwarzschild-AdS result, while the other may become superluminal. Aside from the logarithmic behavior of the scrambling time which indicates chaos, the Lyapunov exponent is also positive and bounded by $\kappa=2\pi T_H/(1-\mu\mathcal{L})$. The Kerr-NUT-AdS and Kerr-Sen-AdS solutions are used as examples to attain a better understanding of the chaotic phenomena in rotating black holes, especially the ones with extra conserved charges.Comment: 10 pages, 4 figures. Comments are welcom

Analisis Pengaruh Viskositas pada Self-Siphon

Penelitian ini bertujuan untuk mengetahui pengaruh nilai viskositas terhadap terjadinya aliran fluida pada self-siphon secara simulasi. Simulasi dilakukan dengan mempertimbangkan gaya-gaya yang bekerja pada single fluid volume element (SFVE). Persamaan gerak pada masingmasing segmen diselesaikan dengan menerapkan hukum Newton. Persamaan-persamaan diselesaikan secara numerik dengan metode Euler. Parameter fisika yang divariasikan dalam simulasi adalah nilai viskositas fluida, karena viskositas mempengaruhi aliran fluida dalam pipa. Berdasarkan penelitian, nilai viskositas fluida η berpengaruh pada dinamika sistem (yang digambarkan oleh kurva terjadinya aliran fluida) namun tidak signifikan pada diameter yang berbeda. Pada nilai viskositas η yang besar, diperlukan panjang pipa yang tercelup dalam fluida (L) yang besar pula. Besarnya panjang pipa L akan memperbesar nilai tekanan hidrostatis sehingga terjadi aliran pada self-siphon